NEET Solved Paper 2014 Question 25
Question: In a region, the potential is represented by V (x, v, z) = 6x - 8xy - 8y + 6yz, where V is in volts and x, y, z are in metres. The electric force experienced by a charge of 2 coulomb situated at point (1, 1, 1) is [AIPMT 2014]
Options:
A) $ 6\sqrt{5}N $
B) 30 N
C) 24 N
D) $ 4\sqrt{35}N $
Show Answer
Answer:
Correct Answer: D
Solution:
- We know $ F=qE $ ?(i) $ E=-\frac{dv}{dr} $ $ . \begin{cases} & E _{x}\frac{\delta V}{\delta x}=6-8y \\ & E _{y}=\frac{\delta V}{\delta y}=-8x-8+6z \\ \end{cases} $
(ii) $ E _{z}=6y $ Above values of $ E _{x},E _{y} $ , and $ E _{z} $ at (1, 1, 1) are $ E _{x}=6-8\times (1)=-2 $ $ E _{y}=-8(1)-8+6(1)=-10 $ $ E _{z}=6\times 1=6 $
So, $ E _{net}=\sqrt{{{(-2)}^{2}}+{{(10)}^{2}}+{{(6)}^{2}}} $ $ =\sqrt{4+100+36}=\sqrt{40}\Rightarrow \sqrt{35\times 4} $ $ =2\sqrt{35}N/C $
So, $ F=q,E _{net}=2(2\sqrt{35})=4\sqrt{35}N $
